Numerical solution of stress intensity factors of multiple cracks in great number with eigen COD boundary integral equations

Based on the eigen crack opening displacement (COD) boundary integral equations, a newly developed computational approach is proposed for the analysis of multiple crack problems. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix. The interactions among cracks are dealt with by two parts according to the distances of cracks to the current crack. The strong effects of cracks in adjacent group are treated with the aid of the local Eshelby matrix derived from the traction BIEs in discrete form. While the relatively week effects of cracks in far-field group are treated in the iteration procedures. Numerical examples are provided for the stress intensity factors of multiple cracks, up to several thousands in number, with the proposed approach. By comparing with the analytical solutions in the literature as well as solutions of the dual boundary integral equations, the effectiveness and the efficiencies of the proposed approach are verified.

Exponential asymptotics of free surface flow due to a line source

The steady problem of free surface flow due to a submerged line source is revisited for the case in which the fluid depth is finite and there is a stagnation point on the free surface directly above the source. Both the strength of the source and the fluid speed in the far field are measured by a dimensionless parameter, the Froude number. By applying techniques in exponential asymptotics, it is shown that there is a train of periodic waves on the surface of the fluid with an amplitude which is exponentially small in the limit that the Froude number vanishes. This study clarifies that periodic waves do form for flows due to a source, contrary to a suggestion by Chapman & Vanden-Broeck (2006, J. Fluid Mech., 567, 299--326). The exponentially small nature of the waves means they appear beyond all orders of the original power series expansion; this result explains why attempts at describing these flows using a finite number of terms in an algebraic power series incorrectly predict a flat free surface in the far field.

Efficient solution of multiple cracks in great number using eigen COD boundary integral equations with iteration procedure

A newly developed computational approach is proposed in the paper for the analysis of multiple crack problems based on the eigen crack opening displacement (COD) boundary integral equations. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix to determine all the unknown CODs step by step. To deal with the interactions among cracks for multiple crack problems, all cracks in the problem are divided into two groups, namely the adjacent group and the far-field group, according to the distance to the current crack in consideration. The adjacent group contains cracks with relatively small distances but strong effects to the current crack, while the others, the cracks of far-field group are composed of those with relatively large distances. Correspondingly, the eigen COD of the current crack is computed in two parts. The first part is computed by using the fictitious tractions of adjacent cracks via the local Eshelby matrix derived from the traction boundary integral equations in discretized form, while the second part is computed by using those of far-field cracks so that the high computational efficiency can be achieved in the proposed approach. The numerical results of the proposed approach are compared not only with those using the dual boundary integral equations (D-BIE) and the BIE with numerical Green's functions (NGF) but also with those of the analytical solutions in literature. The effectiveness and the efficiency of the proposed approach is verified. Numerical examples are provided for the stress intensity factors of cracks, up to several thousands in number, in both the finite and infinite plates.

Post-glacial sea-level changes around the Australian margin : a review

It has been known since Rhodes Fairbridge’s first attempt to establish a global pattern of Holocene sea-level change by combining evidence from Western Australia and from sites in the northern hemisphere that the details of sea-level history since the Last Glacial Maximum vary considerably across the globe. The Australian region is relatively stable tectonically and is situated in the ‘far-field’ of former ice sheets. It therefore preserves important records of post-glacial sea levels that are less complicated by neotectonics or glacio-isostatic adjustments. Accordingly, the relative sea-level record of this region is dominantly one of glacio-eustatic (ice equivalent) sea-level changes. The broader Australasian region has provided critical information on the nature of post-glacial sea level, including the termination of the Last Glacial Maximum when sea level was approximately 125 m lower than present around 21,000–19,000 years BP, and insights into meltwater pulse 1A between 14,600 and 14,300 cal. yr BP. Although most parts of the Australian continent reveals a high degree of tectonic stability, research conducted since the 1970s has shown that the timing and elevation of a Holocene highstand varies systematically around its margin. This is attributed primarily to variations in the timing of the response of the ocean basins and shallow continental shelves to the increased ocean volumes following ice-melt, including a process known as ocean siphoning (i.e. glacio-hydro-isostatic adjustment processes). Several seminal studies in the early 1980s produced important data sets from the Australasian region that have provided a solid foundation for more recent palaeo-sea-level research. This review revisits these key studies emphasising their continuing influence on Quaternary research and incorporates relatively recent investigations to interpret the nature of post-glacial sea-level change around Australia. These include a synthesis of research from the Northern Territory, Queensland, New South Wales, South Australia and Western Australia. A focus of these more recent studies has been the re-examination of: (1) the accuracy and reliability of different proxy sea-level indicators; (2) the rate and nature of post-glacial sea-level rise; (3) the evidence for timing, elevation, and duration of mid-Holocene highstands; and, (4) the notion of mid- to late Holocene sea-level oscillations, and their basis. Based on this synthesis of previous research, it is clear that estimates of past sea-surface elevation are a function of eustatic factors as well as morphodynamics of individual sites, the wide variety of proxy sea-level indicators used, their wide geographical range, and their indicative meaning. Some progress has been made in understanding the variability of the accuracy of proxy indicators in relation to their contemporary sea level, the inter-comparison of the variety of dating techniques used and the nuances of calibration of radiocarbon ages to sidereal years. These issues need to be thoroughly understood before proxy sea-level indicators can be incorporated into credible reconstructions of relative sea-level change at individual locations. Many of the issues, which challenged sea-level researchers in the latter part of the twentieth century, remain contentious today. Divergent opinions remain about: (1) exactly when sea level attained present levels following the most recent post-glacial marine transgression (PMT); (2) the elevation that sea-level reached during the Holocene sea-level highstand; (3) whether sea-level fell smoothly from a metre or more above its present level following the PMT; (4) whether sea level remained at these highstand levels for a considerable period before falling to its present position; or (5) whether it underwent a series of moderate oscillations during the Holocene highstand.

Mid-Holocene sea-level and coral reef demise : U-Th dating of subfossil corals in Moreton Bay, Australia

It is increasingly apparent that sea-level data (e.g. microfossil transfer functions, dated coral microatolls and direct observations from satellite and tidal gauges) vary temporally and spatially at regional to local scales, thus limiting our ability to model future sea-level rise for many regions. Understanding sealevel response at ‘far-field’ locations at regional scales is fundamental for formulating more relevant sea-level rise susceptibility models within these regions under future global change projections. Fossil corals and reefs in particular are valuable tools for reconstructing past sea levels and possible environmental phase shifts beyond the temporal constraints of instrumental records. This study used abundant surface geochronological data based on in situ subfossil corals and precise elevation surveys to determine previous sea level in Moreton Bay, eastern Australia, a far-field site. A total of 64 U-Th dates show that relative sea level was at least 1.1 m above modern lowest astronomical tide (LAT) from at least ˜6600 cal. yr BP. Furthermore, a rapid synchronous demise in coral reef growth occurred in Moreton Bay ˜5800 cal. yr BP, coinciding with reported reef hiatus periods in other areas around the Indo-Pacific region. Evaluating past reef growth patterns and phases allows for a better interpretation of anthropogenic forcing versus natural environmental/climatic cycles that effect reef formation and demise at all scales and may allow better prediction of reef response to future global change.

Integrating 40Ar-39Ar, 87Rb-87Sr and 147Sm-143Nd geochronology of authigenic illite to evaluate tectonic reactivation in an intraplate setting, central Australia

The Warburton-Cooper basins, central Australia, include a multitude of reactivated fracture-fault networks related to a complex, and poorly understood, tectonic evolution. We investigated authigenic illites from a granitic intrusion and sedimentary rocks associated with prominent structural features (Gidgealpa-Merrimelia-Innamincka Ridge and the Nappamerri Trough). These were analysed by 40Ar-39Ar, 87Rb-87Sr and 147Sm-143Nd geochronology to explore the thermal and tectonic histories of central Australian basins. The combined age data provide evidence for three major periods of fault reactivation throughout the Phanerozoic. While Carboniferous (323.3 ± 9.4 Ma) and Late Triassic ages (201.7 ± 9.3 Ma) derive from basin-wide hydrothermal circulation, Cretaceous ages (~128 to ~86 Ma) reflect episodic fluid flow events restricted to the synclinal Nappamerri Trough. Such events result from regional extensional tectonism derived from the transferral of far-field stresses to mechanically and thermally weakened regions of the Australian continent. Specifically, Cretaceous ages reflect continent-wide transmission of tensional stress from a > 2500 km long rifting event on the Eastern (and southern) Australian margin associated with break-up of Gondwana and opening of the Tasman Sea. By integrating 40Ar-39Ar, 87Rb-87Sr and 147Sm-143Nd dating, this study highlights the use of authigenic illite in temporally constraining the tectonic evolution of intracontinental basins that would otherwise remain unknown. Furthermore, combining Sr- and Ar-isotopic systems enables more accurate dating of authigenesis whilst significantly reducing geochemical pitfalls commonly associated with these radioisotopic dating methods.

Numerical simulation of railway track supporting system using finite-infinite and thin layer elements under impulsive loads

The present study deals with two dimensional, numerical simulation of railway track supporting system subjected to dynamic excitation force. Under plane strain condition, the coupled finite-infinite elements to represent the near and far field stress distribution and thin layer interface element was employed to model the interfacial behavior between sleepers and ballast. To account for the relative debonding, slipping and crushing that could take place in the contact area between the sleepers and ballast, modified Mohr-Coulomb criterion was adopted. Furthermore an attempt has been made to consider the elasto-plastic material non-linearity of the railway track supporting media by employing different constitutive models to represent steel, concrete and supporting materials. Based on the proposed physical and constitutive modeling a code has been developed for dynamic loads. The applicability of the developed F.E code has been demonstrated by analyzing a real railway supporting structure.

Two-dimensional bow and stern flows in a finite-depth fluid with constant vorticity

This thesis is concerned with two-dimensional free surface flows past semi-infinite surface-piercing bodies in a fluid of finite-depth. Throughout the study, it is assumed that the fluid in question is incompressible, and that the effects of viscosity and surface tension are negligible. The problems considered are physically important, since they can be used to model the flow of water near the bow or stern of a wide, blunt ship. Alternatively, the solutions can be interpreted as describing the flow into, or out of, a horizontal slot. In the past, all research conducted on this topic has been dedicated to the situation where the flow is irrotational. The results from such studies are extended here, by allowing the fluid to have constant vorticity throughout the flow domain. In addition, new results for irrotational flow are also presented. When studying the flow of a fluid past a surface-piercing body, it is important to stipulate in advance the nature of the free surface as it intersects the body. Three different possibilities are considered in this thesis. In the first of these possibilities, it is assumed that the free surface rises up and meets the body at a stagnation point. For this configuration, the nonlinear problem is solved numerically with the use of a boundary integral method in the physical plane. Here the semi-infinite body is assumed to be rectangular in shape, with a rounded corner. Supercritical solutions which satisfy the radiation condition are found for various values of the Froude number and the dimensionless vorticity. Subcritical solutions are also found; however these solutions violate the radiation condition and are characterised by a train of waves upstream. In the limit that the height of the body above the horizontal bottom vanishes, the flow approaches that due to a submerged line sink in a $90^\circ$ corner. This limiting problem is also examined as a special case. The second configuration considered in this thesis involves the free surface attaching smoothly to the front face of the rectangular shaped body. For this configuration, nonlinear solutions are computed using a similar numerical scheme to that used in the stagnant attachment case. It is found that these solution exist for all supercritical Froude numbers. The related problem of the cusp-like flow due to a submerged sink in a corner is also considered. Finally, the flow of a fluid emerging from beneath a semi-infinite flat plate is examined. Here the free surface is assumed to detach from the trailing edge of the plate horizontally. A linear problem is formulated under the assumption that the elevation of the plate is close to the undisturbed free surface level. This problem is solved exactly using the Wiener-Hopf technique, and subcritical solutions are found which are characterised by a train of sinusoidal waves in the far field. The nonlinear problem is also considered. Exact relations between certain parameters for supercritical flow are derived using conservation of mass and momentum arguments, and these are confirmed numerically. Nonlinear subcritical solutions are computed, and the results are compared to those predicted by the linear theory.

New routes for the field trip

As with the broader field of education research, most writing on the subject of school excursions and field trips has centred around progressive/humanist concerns for building pupil’s self-esteem and for the development of the ‘whole child’. Such research has also stressed the importance of a broad, grounded, and experiential curriculum - as exemplified by subjects containing these extra-school activities - as well as the possibility of strengthening the relationship between student and teacher. Arguing that this approach to the field trip is both exhausted of ideas and conceptually flawed, this paper proposes some alternate routes into the area for the prospective researcher. First, it is argued that by historicising the subject matter, it can be seen that school excursions are not simply the product of the contemporary humanist desire for diverse and fulfilling educational experiences, rather they can, in part, be traced to eighteenth century beliefs among the English gentry that travel formed a crucial component of a good education, to the advent of an affordable public rail system, and to school tours associated with the Temperance movement. Second, field trips can be understood from within the associated framework of concerns over the governance of tourism and the organisation of disciplinary apparatuses for the production of an educated and regulated citizenry. Far from being a simple learning experience, museums and art galleries form part of a complex of disciplinary and power relations designed to produce a populace with very specific capacities, aspirations and styles of public conduct. Finally, rather than allowing children ‘freedom’ from the constraints of the classroom, on the contrary, through the medium of the field-trip, children can become accustomed to having their activities governed in the broader domain of the generalised community . School excursions thereby constitute an effective tactic through which young people have their conduct managed, and their social and scholastic identities shaped and administered.

Avoiding full extension field arithmetic in pairing computations

The most costly operations encountered in pairing computations are those that take place in the full extension field Fpk . At high levels of security, the complexity of operations in Fpk dominates the complexity of the operations that occur in the lower degree subfields. Consequently, full extension field operations have the greatest effect on the runtime of Miller’s algorithm. Many recent optimizations in the literature have focussed on improving the overall operation count by presenting new explicit formulas that reduce the number of subfield operations encountered throughout an iteration of Miller’s algorithm. Unfortunately, almost all of these improvements tend to suffer for larger embedding degrees where the expensive extension field operations far outweigh the operations in the smaller subfields. In this paper, we propose a new way of carrying out Miller’s algorithm that involves new explicit formulas which reduce the number of full extension field operations that occur in an iteration of the Miller loop, resulting in significant speed ups in most practical situations of between 5 and 30 percent.

Experimental study of the concentration field of discharge from a boat propeller

Two-stroke outboard boat engines using total loss lubrication deposit a significant proportion of their lubricant and fuel directly into the water. The purpose of this work is to document the velocity and concentration field characteristics of a submerged swirling water jet emanating from a propeller in order to provide information on its fundamental characteristics. The properties of the jet were examined far enough downstream to be relevant to the eventual modelling of the mixing problem. Measurements of the velocity and concentration field were performed in a turbulent jet generated by a model boat propeller (0.02 m diameter) operating at 1500 rpm and 3000 rpm in a weak co-flow of 0.04 m/s. The measurements were carried out in the Zone of Established Flow up to 50 propeller diameters downstream of the propeller, which was placed in a glass-walled flume 0.4 m wide with a free surface depth of 0.15 m. The jet and scalar plume development were compared to that of a classical free round jet. Further, results pertaining to radial distribution, self similarity, standard deviation growth, maximum value decay and integral fluxes of velocity and concentration were presented and fitted with empirical correlations. Furthermore, propeller induced mixing and pollutant source concentration from a two-stroke engine were estimated.

Visual sensitivity loss in the central thirty degrees of visual field is associated with diabetic peripheral neuropathy

Aims/hypothesis: Impaired central vision has been shown to predict diabetic peripheral neuropathy (DPN). Several studies have demonstrated diffuse retinal neurodegenerative changes in diabetic patients prior to retinopathy development, raising the prospect that non-central vision may also be compromised by primary neural damage. We hypothesise that type 2 diabetic patients with DPN exhibit visual sensitivity loss in a distinctive pattern across the visual field, compared with a control group of type 2 diabetic patients without DPN. Methods: Increment light sensitivity was measured by standard perimetry in the central 30 degree of visual field for two age-matched groups of type 2 diabetic patients, with and without neuropathy (n=40/30). Neuropathy status was assigned using the neuropathy disability score. Mean visual sensitivity values were calculated globally, for each quadrant and for three eccentricities (0-10 degree , 11-20 degree and 21-30 degree ). Data were analysed using a generalised additive mixed model (GAMM). Results: Global and quadrant between-group visual sensitivity mean differences were marginally but consistently lower (by about 1 dB) in the neuropathy cohort compared with controls. Between-group mean differences increased from 0.36 to 1.81 dB with increasing eccentricity. GAMM analysis, after adjustment for age, showed these differences to be significant beyond 15 degree eccentricity and monotonically increasing. Retinopathy levels and disease duration were not significant factors within the model (p=0.90). Conclusions/interpretation: Visual sensitivity reduces disproportionately with increasing eccentricity in type 2 diabetic patients with peripheral neuropathy. This sensitivity reduction within the central 30 degree of visual field may be indicative of more consequential loss in the far periphery.

An interpretive field study of packaged software selection processes

Packaged software is pre-built with the intention of licensing it to users in domestic settings and work organisations. This thesis focuses upon the work organisation where packaged software has been characterised as one of the latest ‘solutions’ to the problems of information systems. The study investigates the packaged software selection process that has, to date, been largely viewed as objective and rational. In contrast, this interpretive study is based on a 21⁄2 year long field study of organisational experiences with packaged software selection at T.Co, a consultancy organisation based in the United Kingdom. Emerging from the iterative process of case study and action research is an alternative theory of packaged software selection. The research argues that packaged software selection is far from the rationalistic and linear process that previous studies suggest. Instead, the study finds that aspects of the traditional process of selection incorporating the activities of gathering requirements, evaluation and selection based on ‘best fit’ may or may not take place. Furthermore, even where these aspects occur they may not have equal weight or impact upon implementation and usage as may be expected. This is due to the influence of those multiple realities which originate from the organisational and market environments within which packages are created, selected and used, the lack of homogeneity in organisational contexts and the variously interpreted characteristics of the package in question.

A practical and theoretical definition of 'small field'

Introduction The consistency of measuring small field output factors is greatly increased by reporting the measured dosimetric field size of each factor, as opposed to simply stating the nominal field size [1] and therefore requires the measurement of cross-axis profiles in a water tank. However, this makes output factor measurements time consuming. This project establishes at which field size the accuracy of output factors are not affected by the use of potentially inaccurate nominal field sizes, which we believe establishes a practical working definition of a ‘small’ field. The physical components of the radiation beam that contribute to the rapid change in output factor at small field sizes are examined in detail. The physical interaction that dominates the cause of the rapid dose reduction is quantified, and leads to the establishment of a theoretical definition of a ‘small’ field. Methods Current recommendations suggest that radiation collimation systems and isocentre defining lasers should both be calibrated to permit a maximum positioning uncertainty of 1 mm [2]. The proposed practical definition for small field sizes is as follows: if the output factor changes by ±1.0 % given a change in either field size or detector position of up to ±1 mm then the field should be considered small. Monte Carlo modelling was used to simulate output factors of a 6 MV photon beam for square fields with side lengths from 4.0 to 20.0 mm in 1.0 mm increments. The dose was scored to a 0.5 mm wide and 2.0 mm deep cylindrical volume of water within a cubic water phantom, at a depth of 5 cm and SSD of 95 cm. The maximum difference due to a collimator error of ±1 mm was found by comparing the output factors of adjacent field sizes. The output factor simulations were repeated 1 mm off-axis to quantify the effect of detector misalignment. Further simulations separated the total output factor into collimator scatter factor and phantom scatter factor. The collimator scatter factor was further separated into primary source occlusion effects and ‘traditional’ effects (a combination of flattening filter and jaw scatter etc.). The phantom scatter was separated in photon scatter and electronic disequilibrium. Each of these factors was plotted as a function of field size in order to quantify how each affected the change in small field size. Results The use of our practical definition resulted in field sizes of 15 mm or less being characterised as ‘small’. The change in field size had a greater effect than that of detector misalignment. For field sizes of 12 mm or less, electronic disequilibrium was found to cause the largest change in dose to the central axis (d = 5 cm). Source occlusion also caused a large change in output factor for field sizes less than 8 mm. Discussion and conclusions The measurement of cross-axis profiles are only required for output factor measurements for field sizes of 15 mm or less (for a 6 MV beam on Varian iX linear accelerator). This is expected to be dependent on linear accelerator spot size and photon energy. While some electronic disequilibrium was shown to occur at field sizes as large as 30 mm (the ‘traditional’ definition of small field [3]), it has been shown that it does not cause a greater change than photon scatter until a field size of 12 mm, at which point it becomes by far the most dominant effect.

Modeling and sensorless direct torque and flux control of a dual-airgap axial flux permanent-magnet machine with field-weakening operation

This paper presents the modeling and motion-sensorless direct torque and flux control of a novel dual-airgap axial-flux permanent-magnet machine optimized for use in flywheel energy storage system (FESS) applications. Independent closed-loop torque and stator flux regulation are performed in the stator flux ( x-y) reference frame via two PI controllers. This facilitates fast torque dynamics, which is critical as far as energy charging/discharging in the FESS is concerned. As FESS applications demand high-speed operation, a new field-weakening algorithm is proposed in this paper. Flux weakening is achieved autonomously once the y-axis voltage exceeds the available inverter voltage. An inherently speed sensorless stator flux observer immune to stator resistance variations and dc-offset effects is also proposed for accurate flux and speed estimation. The proposed observer eliminates the rotary encoder, which in turn reduces the overall weight and cost of the system while improving its reliability. The effectiveness of the proposed control scheme has been verified by simulations and experiments on a machine prototype.